Calculating the expectation and variance of the present value for a random profit stream of uncertain duration

Yigal Gerchak, Thomas Åstebro

Research output: Contribution to journalArticlepeer-review

Abstract

We derive the mean and variance of the random discounted sum ∑n=1Nθnχn When N is uncertain, as are the χn's. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.

Original languageEnglish
Pages (from-to)339-349
Number of pages11
JournalEngineering Economist
Volume45
Issue number4
DOIs
StatePublished - 2000
Externally publishedYes

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